On positive solution for a class of quasilinear elliptic systems with sign-changing weights

Abstract

In this paper, we consider the problem for the existence of positive solutions of quasi- linear elliptic system ⎧ ⎪ ⎪ −Δpu = λa(x)u α v γ , x ∈ Ω, −Δqv = λb(x)u η v β , x ∈ Ω, u = v = 0, x ∈ ∂ Ω, where the λ > 0i s ap arameter,Ω is a bounded domain in RN(N > 1) with smooth bound- ary ∂ Ω ,a nd theΔpz = div(|∇z| p−2 ∇z) is the p-Laplacian operator. Here a(x) and b(x) are C 1 sign-changing functions that maybe are negative near the boundary. Using the method of sub-super solutions and comparison principle, which studied the existence of positive solutions for quasilinear elliptic system. The main results of the present paper are new and extend the previously known results.